Sigma, the first single-round group membership (GM) algorithm, was recently introduced and demonstrated to operate consistently with theoretical expectations in a simulated WAN environment. Sigma achieved similar quality of membership configurations as existing algorithms but required fewer message exchange rounds. We now consider Sigma in terms of scalability. Sigma involves all-to-all (A2A) type of communication among members. A2A protocols have been shown to perform worse than leader-based (LB) protocols in certain networks, due to greater message overhead and higher likelihood of message loss. Thus, although LB protocols often involve additional communication steps, they can be more efficient in practice, particularly in fault-prone networks with large numbers of participating nodes. In this paper, we present Leader-Based Sigma, which transforms the original all-to-all version into a more scalable centralized communication scheme, and discuss the rounds vs. messages tradeoff involved in optimizing GM algorithms for deployment in large-scale, fault-prone dynamic network environments.